"Palestine is the cradle of the three monotheistic faiths. We stand strongly against any attack on any religion," Abbas said in a statement.
In apparently unscripted Arabic remarks to the European Parliament on Thursday, Abbas said that recently "a number of rabbis in Israel made a clear declaration and asked their government to poison water to kill the Palestinians".
He gave no source for the accusation, but said it was part of wider Israeli campaign of incitement against the Palestinians.
Israeli Prime Minister Benjamin Netanyahu's office responded by accusing Abbas of disseminating "a blood libel in front of the European Parliament".
Abbas's office acknowledged on Saturday that the reports on which his comments had been based had proved without foundation.
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"It has become evident that the alleged statements by a rabbi on poisoning Palestinian wells, which were reported by various media outlets, are baseless," it said.
Abbas "didn't intend to do harm to Judaism or to offend Jewish people around the world".
The accusation that Jews were poisoning the wells of Christians gained traction in 14th century Europe as a plague swept across the continent.
Another allegation from the Middle Ages -- that Jews murdered Christian children to use their blood for ritual purposes -- gave rise to the term "blood libel".
The Jerusalem Post newspaper reported on Tuesday that the well-poisoning story had resurfaced in a statement by the Palestinian foreign ministry naming a "rabbi Mlad" as authorising contamination of Palestinian water.
The Post and other Israeli media said they had failed to locate any such person or edict.